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Michael Newman

Publications and source records attributed to Michael Newman.

34 records · Page 2Linked to original sources
arXiv2020

Generating Fault-Tolerant Cluster States from Crystal Structures

Measurement-based quantum computing (MBQC) is a promising alternative to traditional circuit-based quantum computing predicated on the construction and measurement of cluster states. Recent work has demonstrated that MBQC provides a more general framework for fault-tolerance that extends beyond foliated quantum error-correcting codes. We systematically expand on that paradigm, and use combinatorial tiling theory to study and construct new examples of fault-tolerant cluster states derived from crystal structures. Included among these is a robust self-dual cluster state requiring only degree-3 connectivity. We benchmark several of these cluster states in the presence of circuit-level noise, and find a variety of promising candidates whose performance depends on the specifics of the noise model. By eschewing the distinction between data and ancilla, this malleable framework lays a foundation for the development of creative and competitive fault-tolerance schemes beyond conventional error-correcting codes.

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arXiv2020

Classical Simulation of Quantum Supremacy Circuits

It is believed that random quantum circuits are difficult to simulate classically. These have been used to demonstrate quantum supremacy: the execution of a computational task on a quantum computer that is infeasible for any classical computer. The task underlying the assertion of quantum supremacy by Arute et al. (Nature, 574, 505--510 (2019)) was initially estimated to require Summit, the world's most powerful supercomputer today, approximately 10,000 years. The same task was performed on the Sycamore quantum processor in only 200 seconds. In this work, we present a tensor network-based classical simulation algorithm. Using a Summit-comparable cluster, we estimate that our simulator can perform this task in less than 20 days. On moderately-sized instances, we reduce the runtime from years to minutes, running several times faster than Sycamore itself. These estimates are based on explicit simulations of parallel subtasks, and leave no room for hidden costs. The simulator's key ingredient is identifying and optimizing the "stem" of the computation: a sequence of pairwise tensor contractions that dominates the computational cost. This orders-of-magnitude reduction in classical simulation time, together with proposals for further significant improvements, indicates that achieving quantum supremacy may require a period of continuing quantum hardware developments without an unequivocal first demonstration.

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arXiv2020

Fault-Tolerant Weighted Union-Find Decoding on the Toric Code

Quantum error correction requires decoders that are both accurate and efficient. To this end, union-find decoding has emerged as a promising candidate for error correction on the surface code. In this work, we benchmark a weighted variant of the union-find decoder on the toric code under circuit-level depolarizing noise. This variant preserves the almost-linear time complexity of the original while significantly increasing the performance in the fault-tolerance setting. In this noise model, weighting the union-find decoder increases the threshold from 0.38% to 0.62%, compared to an increase from 0.65% to 0.72% when weighting a matching decoder. Further assuming quantum non-demolition measurements, weighted union-find decoding achieves a threshold of 0.76% compared to the 0.90% threshold when matching. We additionally provide comparisons of timing as well as low error rate behavior.

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arXiv2020

Alibaba Cloud Quantum Development Platform: Surface Code Simulations with Crosstalk

We report, in a sequence of notes, our work on the Alibaba Cloud Quantum Development Platform (AC-QDP). AC-QDP provides a set of tools for aiding the development of both quantum computing algorithms and quantum processors, and is powered by a large-scale classical simulator deployed on Alibaba Cloud. In this note, we simulate a distance-3 logical qubit encoded in the 17-qubit surface code using experimental noise parameters for transmon qubits in a planar circuit QED architecture. Our simulation features crosstalk induced by ZZ-interactions. We show that at the current-stage noise levels, crosstalk contributes significantly to the dephasing of the logical qubit. This results in a total phase-flip probability of $\sim 0.6\%$, about $60\%$ higher than expected without considering crosstalk. This indicates that for the code considered, the current noise parameters approach, but do not yet meet, the break-even fault-tolerance regime.

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arXiv2019

Alibaba Cloud Quantum Development Platform: Large-Scale Classical Simulation of Quantum Circuits

We report, in a sequence of notes, our work on the Alibaba Cloud Quantum Development Platform(AC-QDP). AC-QDP provides a set of tools for aiding the development of both quantum computing algorithms and quantum processors, and is powered by a large-scale classical simulator deployed on Alibaba Cloud. In this note, we report the computational experiments demonstrating the classical simulation capability of AC-QDP. We use as a benchmark the random quantum circuits designed for Google's Bristlecone QPU {\cite{GRCS}}. We simulate Bristlecone-70 circuits with depth $1 + 32 + 1$ in $0.43$ second per amplitude, using $1449$ Alibaba Cloud Elastic Computing Service (ECS) instances, each with $88$ Intel Xeon(Skylake) Platinum 8163 vCPU cores @ 2.5 GHz and $160$ gigabytes of memory. By comparison, the previously best reported results for the same tasks are $104$ and $135$ seconds, using NASA's HPC Pleiades and Electra systems, respectively ({arXiv:1811.09599}). Furthermore, we report simulations of Bristlecone-70 with depth $1+36+1$ and depth $1+40+1$ in $5.6$ and $580.7$ seconds per amplitude, respectively. To the best of our knowledge, these are the first successful simulations of instances at these depths.

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arXiv2019

Handling Leakage with Subsystem Codes

Leakage is a particularly damaging error that occurs when a qubit state falls out of its two-level computational subspace. Compared to independent depolarizing noise, leaked qubits may produce many more configurations of harmful correlated errors during error-correction. In this work, we investigate different local codes in the low-error regime of a leakage gate error model. When restricting to bare-ancilla extraction, we observe that subsystem codes are good candidates for handling leakage, as their locality can limit damaging correlated errors. As a case study, we compare subspace surface codes to the subsystem surface codes introduced by Bravyi et al. In contrast to depolarizing noise, subsystem surface codes outperform same-distance subspace surface codes below error rates as high as $\lessapprox 7.5 \times 10^{-4}$ while offering better per-qubit distance protection. Furthermore, we show that at low to intermediate distances, Bacon-Shor codes offer better per-qubit error protection against leakage in an ion-trap motivated error model below error rates as high as $\lessapprox 1.2 \times 10^{-3}$. For restricted leakage models, this advantage can be extended to higher distances by relaxing to unverified two-qubit cat state extraction in the surface code. These results highlight an intrinsic benefit of subsystem code locality to error-corrective performance.

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arXiv2018

Stabilizer Slicing: Coherent Error Cancellations in LDPC Codes

Coherent errors are a dominant noise process in many quantum computing architectures. Unlike stochastic errors, these errors can combine constructively and grow into highly detrimental overrotations. To combat this, we introduce a simple technique for suppressing systematic coherent errors in low-density parity-check (LDPC) stabilizer codes, which we call stabilizer slicing. The essential idea is to slice low-weight stabilizers into two equally-weighted Pauli operators and then apply them by rotating in opposite directions, causing their overrotations to interfere destructively on the logical subspace. With access to native gates generated by 3-body Hamiltonians, we can completely eliminate purely coherent overrotation errors, and for overrotation noise of 0.99 unitarity we achieve a 135-fold improvement in the logical error rate of Surface-17. For more conventional 2-body ion trap gates, we observe an 89-fold improvement for Bacon-Shor-13 with purely coherent errors which should be testable in near-term fault-tolerance experiments. This second scheme takes advantage of the prepared gauge degrees of freedom, and to our knowledge is the first example in which the state of the gauge directly affects the robustness of a code's memory. This work demonstrates that coherent noise is preferable to stochastic noise within certain code and gate implementations when the coherence is utilized effectively.

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arXiv2018

2-D Compass Codes

The compass model on a square lattice provides a natural template for building subsystem stabilizer codes. The surface code and the Bacon-Shor code represent two extremes of possible codes depending on how many gauge qubits are fixed. We explore threshold behavior in this broad class of local codes by trading locality for asymmetry and gauge degrees of freedom for stabilizer syndrome information. We analyze these codes with asymmetric and spatially inhomogeneous Pauli noise in the code capacity and phenomenological models. In these idealized settings, we observe considerably higher thresholds against asymmetric noise. At the circuit level, these codes inherit the bare-ancilla fault-tolerance of the Bacon-Shor code.

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arXiv2018

Further Limitations on Information-Theoretically Secure Quantum Homomorphic Encryption

In this brief note, we review and extend existing limitations on information-theoretically (IT) secure quantum fully homomorphic encryption (QFHE). The essential ingredient remains Nayak's bound, which provides a tradeoff between the number of homomorphically implementable functions of an IT-secure QHE scheme and its efficiency. Importantly, the bound is robust to imperfect IT-security guarantees. We summarize these bounds in the context of existing QHE schemes, and discuss subtleties of the imposed restrictions.

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arXiv2018

Classical Simulation of Intermediate-Size Quantum Circuits

We introduce a distributed classical simulation algorithm for general quantum circuits, and present numerical results for calculating the output probabilities of universal random circuits. We find that we can simulate more qubits to greater depth than previously reported using the cluster supported by the Data Infrastructure and Search Technology Division of the Alibaba Group. For example, computing a single amplitude of an $8\times 8$ qubit circuit with depth $40$ was previously beyond the reach of supercomputers. Our algorithm can compute this within $2$ minutes using a small portion ($\approx$ 14% of the nodes) of the cluster. Furthermore, by successfully simulating quantum supremacy circuits of size $9\times 9\times 40$, $10\times 10\times 35 $, $11\times 11\times 31$, and $12\times 12\times 27 $, we give evidence that noisy random circuits with realistic physical parameters may be simulated classically. This suggests that either harder circuits or error-correction may be vital for achieving quantum supremacy from random circuit sampling.

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arXiv2018

Explicit lower bounds on strong quantum simulation

We consider the problem of strong (amplitude-wise) simulation of $n$-qubit quantum circuits, and identify a subclass of simulators we call monotone. This subclass encompasses almost all prominent simulation techniques. We prove an unconditional (i.e. without relying on any complexity theoretic assumptions) and explicit $(n-2)(2^{n-3}-1)$ lower bound on the running time of simulators within this subclass. Assuming the Strong Exponential Time Hypothesis (SETH), we further remark that a universal simulator computing any amplitude to precision $2^{-n}/2$ must take at least $2^{n - o(n)}$ time. Finally, we compare strong simulators to existing SAT solvers, and identify the time-complexity below which a strong simulator would improve on state-of-the-art SAT solving.

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arXiv2018

Transversal switching between generic stabilizer codes

We propose a randomized variant of the stabilizer rewiring algorithm (SRA), a method for constructing a transversal circuit mapping between any pair of stabilizer codes. As gates along this circuit are applied, the initial code is deformed through a series of intermediate codes before reaching the final code. With this randomized variant, we show that there always exists a path of deformations which preserves the code distance throughout the circuit, while using at most linear overhead in the distance. Furthermore, we show that a random path will almost always suffice, and discuss prospects for implementing general fault-tolerant code switching circuits.

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arXiv2017

Limitations on Transversal Computation through Quantum Homomorphic Encryption

Transversality is a simple and effective method for implementing quantum computation fault-tolerantly. However, no quantum error-correcting code (QECC) can transversally implement a quantum universal gate set (Eastin and Knill, Phys. Rev. Lett., 102, 110502). Since reversible classical computation is often a dominating part of useful quantum computation, whether or not it can be implemented transversally is an important open problem. We show that, other than a small set of non-additive codes that we cannot rule out, no binary QECC can transversally implement a classical reversible universal gate set. In particular, no such QECC can implement the Toffoli gate transversally. We prove our result by constructing an information theoretically secure (but inefficient) quantum homomorphic encryption (ITS-QHE) scheme inspired by Ouyang et al. (arXiv:1508.00938). Homomorphic encryption allows the implementation of certain functions directly on encrypted data, i.e. homomorphically. Our scheme builds on almost any QECC, and implements that code's transversal gate set homomorphically. We observe a restriction imposed by Nayak's bound (FOCS 1999) on ITS-QHE, implying that any ITS quantum fully homomorphic scheme (ITS-QFHE) implementing the full set of classical reversible functions must be highly inefficient. While our scheme incurs exponential overhead, any such QECC implementing Toffoli transversally would still violate this lower bound through our scheme.

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arXiv2014

On the knot Floer filtration of the concordance group

The knot Floer complex together with the associated concordance invariant epsilon can be used to define a filtration on the smooth concordance group. We show that the indexing set of this filtration contains the natural numbers cross the integers as an ordered subset.

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